A chain of mean value inequalities
Applicable Analysis and Discrete Mathematics, 2020 G = G(x, y) = ?xy, L = L(x,y) = x?y/log(x)?log(y)'' I=I(x,y)= 1/e(xx/yy) 1/(x-y), A=A(x.y)=x+y/2, be the geometric, logarithmic, identric, and arithmetic means of x and y.
H. Alzer, M. Kam
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Hermite‐Hadamard and Simpson‐Like Type Inequalities for Differentiable Harmonically Convex Functions
Journal of Mathematics, Volume 2014, Issue 1, 2014., 2014 A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite‐Hadamard and Simpson‐like types for functions whose derivatives in absolute value at certain power are harmonically convex.
İmdat İşcan, Roberto A. Kraenkel
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New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals
International Journal of Analysis, Volume 2014, Issue 1, 2014., 2014 The author obtains new estimates on generalization of Hadamard, Ostrowski, and Simpson type inequalities for Lipschitzian functions via Hadamard fractional integrals. Some applications to special means of positive real numbers are also given.
İmdat İşcan, Julien Salomon
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Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
, 1999 We report the results of certain integrations of quantum-theoretic interest, relying, in this regard, upon recently developed parameterizations of Boya et al of the n x n density matrices, in terms of squared components of the unit (n-1)-sphere and the n
Bateman P T +46 more
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Sharp Inequalities for Trigonometric Functions
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We establish several sharp inequalities for trigonometric functions and present their corresponding inequalities for bivariate means.
Zhen-Hang Yang +4 more
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On Trapezoid Inequality Via a Grüss Type Result and Applications [PDF]
, 1999 In this paper, we point out a Grüss type inequality and apply it for special means (logarithmic mean, identric mean, etc...
Dragomir, Sever S, McAndrew, Alasdair
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Some sharp inequalities involving Seiffert and other means and their concise proofs [PDF]
, 2012 In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic ...
Jiang, Wei-Dong, Qi, Feng
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Integral representations of bivariate complex geometric mean and their applications
Journal of Computational and Applied Mathematics, 2018 In the paper, the authors survey integral representations (including the Levy–Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky’s mean, the harmonic mean, the (weighted ...
Feng Qi (祁锋), D. Lim
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A Class of Logarithmically Completely Monotonic Functions and Their Applications
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 We study the recent investigations on a class of functions which are logarithmically completely monotonic. Two open problems are also presented.
Senlin Guo, Qiu-Ming Luo
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Optimal Lower Generalized Logarithmic Mean Bound for the Seiffert Mean
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 We present the greatest value p such that the inequality P(a, b) > Lp(a, b) holds for all a, b > 0 with a ≠ b, where P(a, b) and Lp(a, b) denote the Seiffert and pth generalized logarithmic means of a and b, respectively.
Ying-Qing Song +4 more
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